The double-click solution I attached earlier is almost entirely played by using the double-click method.
There are a few boxes I have to move it out of the way (by one or two squares) so that the rest of the boxes can move freely.
Overall, it's quick to solve the level using this method.
And I always enabled the "IM" (Instant Moves) selection so that I don't see any of the in-between moves. I see the box moved from point A to B instantly.
That explains it. I do not have, and have never used YSokoban. I will look into this, but I think it best to not endorse any specific method of solution.
Obviously, if you follow the storyline, the double-click method will not solve the puzzle in the manner described. While there is no hard and fast rule that requires solution according to the story line, it does affect the difficulty of solution to not follow it. In that regard, the Hundred puzzle is not difficult, just time-consuming.
I did make a version of the puzzle playable on Lee Haywood's Crossoban site using the Interlock style of filters and associated blocks to segregate the boxes and targets into groups. Using this version of the file you are more forced to follow the storyline, yet you can still change the order you move the boxes in and the targets you place them on. This level must be pasted into the Crossoban import page, as it is not included in the list of available puzzles to play. The level data is below, for those interested in seeing this version.